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It's supposed to be able to move around without tilting. I sort of getting, but struggling to fully come to grips with it. I imagine it can work, I just wonder how well. It certainly can't be good for efficiency.

maybe you have seen beginner planes using lots of dihedral for stabilization. Imagine an extreme case where left and right wing when viewed from the front have a 90° angle, or in other words left and right wing stick out at 45° from the fuselage. If the plane rolls 45° to the left, the left wing is horizontal, while the right wing is vertical. The big difference in lift will push the left wing back in its 'original' position. As a copter can move in all directions, it needs this funnel arrangement to have the same effect. Basically you help your FC with aerodynamic stabilization.

To yaw a copter you usually use left and right turning props to create momentum. The speed around the yaw axis in traditional copters is usually not very fast compared to helicopters. If you want to increase this you need more power. Looking at sin / cos for small angles you will recognize you get 'a lot' of horizontal power with a minimum of vertical loss in lift by rotating the motor arm some degrees.

As soon as you add either windy / gusty conditions or requirements for rapid maneuvering it will break down.

I am sure it does have legitimate application and it will not work for a quadcopter, 6 or even 8 arms / angles are necessary to make it work.

It is possible that a Y 6 or X 8 could be made to work with motors / props with differing angles, but the inefficiencies would be even higher.

Early multicopters often had the props tilted at an angle or in towards the center in various attempts at increasing stability when the electronic controls were not sufficiently developed for the task.

(They also often resorted to having the CG significantly below the prop center line (pendulum) for the same reason (to slow down the roll / pitch moment).

The claim here is that this multicopter will fly flat rather than responding to roll and pitch movements by actually rolling or pitching.

I have searched the internet extensively on these two concepts of propeller dihedral and propeller twist, and I am unable to find any testing results or research that addresses the question of the impact on efficiency of either one.

The authors of this academic paper that addresses stability did not specifically address the question of efficiency.

I am interested to know if you have tested this question of efficiency for this configuration. The makers of the CyPhy have not published data on efficiency for their concept. I encourage anyone who would like to test the concept to build a quadcopter or hexacopter with dihedral and twist, and also build one without dihedral and twist, and report back on the question of efficiency.

It could just as easily be thought that the FC and ESCs would have to do less work to maintain control and stability and the result might just as easily be that there is no net change in efficiency of flight while hovering. It might also turn out that slow to modest flight speeds would not change in efficiency compared to a drone with a flat rotor design. And surely the cost of stabilizing a camera with gimbal motors would impact the overall flight duration. And, if it can be shown that the gimbal is not needed or the motor on the gimbal could be lighter and draw less current, flight times would be longer. That translates to efficiency.

As the flight speed increases, or the correction demands due to higher winds while in hovering mode increase, there might be a lowering of efficiency. But there simply is no data to know for sure. I wish there were data to look at on this subject of efficiency for drones made with propeller dihedral and propeller twist.